\name{vgm}
\alias{vgm}
\alias{print.variogramModel}
\title{
Generate, or Add to Variogram Model
}
\description{
Generates a variogram model, or adds to an existing model. 
\code{print.variogramModel} prints the essence of a variogram  model.
}
\usage{
vgm(psill, model, range, nugget, add.to, anis, kappa = 0.5)
print.variogramModel(x, ...)
}
\arguments{
\item{psill}{ (partial) sill of the variogram model component }
\item{model}{ model type, e.g. "Exp", "Sph", "Gau", "Mat". Calling vgm() without
a model argument returns the list with available models. }
\item{range}{ range of the variogram model component }
\item{kappa}{ smoothness parameter for the Matern class of variogram 
models }
\item{nugget}{ nugget component of the variogram (this basically adds a nugget
compontent to the model) }
\item{add.to}{ a variogram model to which we want to add a component }
\item{anis}{ anisotropy parameters: see notes below }
\item{x}{ a variogram model to print }
\item{...}{ arguments that will be passed to \code{print}, e.g. \code{digits}
(see examples) }
}
\value{
an object of class \code{variogramModel}, which extends data.frame Called
without a model argument returns a character list with available models.
}
\references{ }
\author{ Edzer J. Pebesma }
\note{ 
Geometric anisotropy can be modelled for each individual simple model
by giving two or five anisotropy parameters, two for two-dimensional
and five for three-dimensional data. In any case, the range defined
is the range in the direction of the strongest correlation, or the
major range. Anisotropy parameters define which direction this is (the
main axis), and how much shorter the range is in (the) direction(s)
perpendicular to this main axis.

In two dimensions, two parameters define an anisotropy ellipse, say
\code{anis = c(45, 0.5)}. The first parameter, \code{30}, refers to
the main axis direction: it is the angle for the principal direction
of continuity (measured in degrees, clockwise from positive Y, North).
The second parameter, \code{0.5}, is the anisotropy ratio, the ratio
of the minor range to the major range (a value between 0 and 1).  So,
in our example, if the range in the major direction (North-East) is 100,
the range in the minor direction (South-East) is 50.

In three dimensions, five values should be given in the form \code{anis
= c(p,q,r,s,t)}.  Now, $p$ is the angle for the principal direction of
continuity (measured in degrees, clockwise from Y, in direction of X),
$q$ is the dip angle for the principal direction of continuity (measured
in positive degrees up from horizontal), $r$ is the third rotation angle
to rotate the two minor directions around the principal direction defined
by $p$ and $q$. A positive angle acts counter-clockwise while looking
in the principal direction. Anisotropy ratios $s$ and $t$ are the ratios
between the major range and each of the two minor ranges. 

(Note that \code{anis = c(p,s)} is equivalent to \code{anis = c(p,0,0,s,1)}.)

The implementation in gstat for 2D and 3D anisotropy was taken from
the gslib (probably 1992) code.  I have seen a paper where it is argued
that the 3D anisotropy code implemented in gslib (en then also in gstat)
is in error, but I have not corrected anything afterwards.
}
\seealso{
\link{show.vgms} to view the available models,
\link{fit.variogram},
\link{variogram.line},
\link{variogram} for the sample variogram.
}
\examples{
vgm(10, "Exp", 300)
x <- vgm(10, "Exp", 300)
vgm(10, "Nug", 0)
vgm(10, "Exp", 300, 4.5)
vgm(10, "Mat", 300, 4.5, kappa = 0.7)
vgm( 5, "Exp", 300, add.to = vgm(5, "Exp", 60, nugget = 2.5))
vgm(10, "Exp", 300, anis = c(30, 0.5))
vgm(10, "Exp", 300, anis = c(30, 10, 0, 0.5, 0.3))
# Matern variogram model:
vgm(1, "Mat", 1, kappa=.3)
x <- vgm(0.39527463, "Sph", 953.8942, nugget = 0.06105141)
x
print(x, digits = 3);
# to see all components, do
print.data.frame(x)
}

\keyword{models}